Question

A light weight boy holds two heavy dumbbells of equal masses with outstretched arms while standing on a turn-table which is rotating at an angular frequency ${\omega }_1$ when the dumbbells are at distance $r_1$ from the axis of rotation. The boy suddenly pulls the dumbbells towards his chest until they are at distance $r_2$ from the axis of rotation. The new angular frequency of rotation ${\omega }_2$ of the turn-table will be equal to

• A. ${\omega }_1\frac{r_2}{r_1}$
• B. ${\omega }_1\frac{r_1^2}{r_2^2}$
• C. ${\omega }_1\frac{r_1}{r_2}$
• D. ${\omega }_1\frac{r_2^2}{r_1^2}$

Answer 1

The correct option is B ${\omega }_1\frac{r_1^2}{r_2^2}$

Use the principle of conservation of angular momentum $I_1{\omega }_1=I_2{\omega }_2$
$\therefore {\omega }_1{r}_1^2={\omega }_2{r}_2^2$
${\omega }_2={\omega }_1\frac{r_1^2}{r_2^2}$